R/projection.R

In TML: Tropical Geometry Tools for Machine Learning

#'Project a point on the tropical projective torus onto a tropical polytope
#'
#'This function projects points in the tropical projective torus onto a max- or
#'min-plus tropical polytope based on tropical distance
#'
#'@param D_s matrix where each row is a point defining a tropical polytope
#'@param D point to be projected onto D_s
#'@param tadd function; max indicates max-plus addition, min indicates min-plus
#'  addition. Defaults to max.
#'@return projection of point D onto the tropical polytope defined by D_s
#'@author David Barnhill \email{david.barnhill@@nps.edu}
#'@export
#' @examples
#'D_s <-matrix(c(0,0,0,0,2,5,0,3,1),3,3,TRUE)
#'D <- c(0,7,-1)
#'project.pi(D_s,D)
#'project.pi(D_s,D,tadd=min)

project.pi<-function(D_s, D, tadd=max){
  dual_tadd <- if(identical(tadd, base::max)) min else max

  d <- dim(D_s)
  lambda <- rep(0, d[1])

  for(i in 1:d[1]) {
    lambda[i] <- dual_tadd(D - D_s[i,])
  }

  x <- rep(0, d[2])
  for(i in 1:d[2]) {
    x[i] <- tadd((lambda+D_s)[, i])
  }

  return(normaliz.vector(x))
}